Exit Gradient in Anisotropic Porous Medium

Solving global problem by considering multitude of local problems: Application to fluid flow in anisotropic porous media using the multipoint flux approximation

Weakly singular integral equations for Darcy's flow in anisotropic porous media

This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow.

An implicit algorithm of solving Navier–Stokes equations to simulate flows in anisotropic porous media

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotropic porous media. In this case, the permeability tensor is made up of two components: anisotropy (variation around a point) which correlates with bedding, and heterogeneity (variation from point- to-point) which correlates with grain size. Introduction Previous studies of directional permeability, have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45 intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45 during drilling and coring. Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability. The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA Darcy's law for flow in porous media in its usual form is where q is the flow rate vector, k is the permeability, mu is the viscosity, V is the vector differential operator, and p is the pressure. SPEJ P. 124ˆ

Work carried out in this paper deals with classic Rayleigh–Bѐnard problem for an unsteady, laminar, viscous incompressible fluid of a horizontal layer heated from below which is extended to the three-dimensional convection in a rectangular box with anisotropic and isotropic porous media rotating with constant angular velocity that is investigated. For the given physical system, seven governing PDEs are transformed to system of non-dimensional ODEs using similarity transformation. The investigation demands to apply Fourier series method to study the characteristic of velocity and temperature for the effect of Taylor number, Rayleigh number and Prandtl number for both isotropic and anisotropic cases. The results of the stream function and isotherms on various parameters have been discussed and found to be good agreement for the physical system.

This work involves a quantitative comparison between diffusion (or electrical conduction) and fluid flow occurring in the principal directions of certain simple anisotropic porous media, namely, clusters of parallel circular (or elliptic) cylindrical fibers. The degrees to which the observed macroscopic properties, permeability, and effective diffusivity (electrical conductivity) depend upon the direction of flow are determined analytically. Systems of parallel fibers are shown to be considerably more anisotropic with respect to fluid flow than with respect to diffusion (or electrical conduction), this effect being very pronounced with flattish fibers. It would not appear that any general analogy exists between diffusion (electrical conduction) and fluid flow occurring within anisotropic porous media.

Permeability distribution in reservoirs is very important for the flow ofwater or oil and gas. In this study, the effects of various heterogeneous permeability distributions on the flow field are simulated using the finite difference technique. We have simulated the flow for two types of heterogeneous distributions, one is Gaussian and the other is self-similar or fractal, the latter being much rougher than the former. The results show that the flow is not sensitive to the roughness of the distribution. In the case of lineated heterogeneities, anisotropy in the flow properties occurs. The anisotropy is not very significant if the lineated highly permeable regions are surrounded by less permeable regions. However, in the case of lineated fractures, where the background permeability is small, the flow is very sensitive to the direction of the lineation, such anisotropy can produce orders of magnitude difference in permeability. Furthermore, it is shown that the degree of anisotropy depends on the connectivity of the fractures. The anisotropy decreases with decreasing connectivity.

Soil Mechanics.- to Soil Mechanics.- Lower bound collapse theorem and lack of normality of strain rate to yield surface for soils.- Proceedings of the Geotechnical Conference OSLO 1968.- The double sliding, free rotating model for granular assemblies.- Photoelastic verification of a mechanical model for the flow of a granular material.- Elasto-plastic version of the double sliding model in undrained simple shear tests.- Improvement of the lowerbound solution for the vertical cut off in a cohesive, frictionless soil.- Application of the calculus of variations to the vertical cut off in cohesive frictionless soil.- A variational fallacy.- Consolidation around pore pressure meters.- Application of stress functions to consolidation problems.- Consolidation models consisting of an assembly of viscous elements or a cavity channel network.- Verification of the use of peak area for the quantitative differential thermal analysis.- A capacitative cell apparatus.- Etude photo-Elastique d'un empilement de disques.- Flow and Transport in Porous Media.- to Flow and Transport in Porous Media.- Singularity distributions for the analysis of multiple-fluid flow through porous media.- Moire patterns of the membrane analogy for ground-water movement applied to multiple fluid flow.- A many-valued hodograph in an interface problem.- Generating functions in the theory of flow through porous media.- Vortex theory for multiple fluid in three dimensions.- The simultaneous flow of fresh and salt water in aquifers of large horizontal extension determined by shear flow and vortex theory.- L'entrainement de particules par le courant intersticiel.- and transverse diffusion in granular Discussion of Longitudinal and transverse diffusion in granular deposits.- Transverse dispersion from an originally sharp fresh-salt interface caused by shear flow.- The tensor character of the dispersion coefficient in anisotropic porous media.- Dispersion in fissured rock.

In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is adopted and a discontinuous Galerkin method (DG) is employed to solve the pressure equation. Capillary effects can be neglected in high-rate flooding scenarios. This allows us to present an improved streamline approach in combination with the one-dimensional front tracking method to solve the transport equation. To handle the high computational costs of the DG approximation, domain decomposition is applied combined with an algebraic multigrid preconditioner to solve the linear system. Special care at the interior interfaces is required and the streamline tracer has to include a dynamic communication strategy. The method is validated in various two- and three-dimensional tests, where comparisons of the solutions in terms of approximation of flow front propagation with standard fully-implicit finite volume methods are provided.

In this paper, our main goal is to present a non-classical MPFA method coupled with a high order finite volume method for the simulation of oil water displacements in heterogeneous and anisotropic petroleum reservoirs using general polygonal meshes. The governing equations are solved using the IMPES (IMplicit Pressure and Explicit Saturation) strategy, where the elliptic pressure equation is discretized by a linear Multipoint Flux Approximation method using Harmonic points (MPFA-H) capable to handle strongly heterogeneous and anisotropic media. Besides, to approximate the advective term that characterizes the hyperbolic saturation equation, we use the Multidimensional Optimal Order Detection (MOOD) method. This technique is based in an “a posteriori” limitation procedure, i.e., the limitation procedure is done after the calculation of “candidate solutions” only where necessary to guarantee certain physical properties such as monotonicity. To show the potential of our finite volume formulation, we solve some benchmark problems found in literature.

Elastodynamic analysis of anisotropic liquid-saturated porous medium due to mechanical sources

Effective parameters for flow in saturated heterogeneous porous media

Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures

Stability of mixed convective Jeffrey fluid flow in anisotropic porous media: LTNE effects and non-linear dynamics